A trapezoid has one pair of parallel sides. Draw a transversal perpendicular to the two parallel sides. The area of the trapezoid is equal to the length (which is the mean length of the two parallel sides) times the width (which is the part of the transversal between the parallel...

f - 5 > 7
f > 12
f < 13
So 12 < f < 13
Try it with 12.5, or any other number between 12 and 13

Rewrite both equations so that x is isolated.
x = 120 + y
x = 150 - y
Since both [120 + y] and [150 - y] are equal to x, they must be equal to each other.
120 + y = 150 - y
2y = 30
y = 15
x = 135
...

Slope is always change in y divided by change in x. This is a simple matter if the function is linear because the ratio never changes, but the function described in your table is not linear. The best you can do is calculate an average slope over a given range of x values. For example,...

Square base = 14 * 14 = 196.
Each of four triangular faces = 1/2 * 14 * 25 = 175.
So total surface area = 896.
So, how did I get the height (25) of the triangular faces?
Think of it as finding the hypotenuse of a right triangle whose legs are...

The triangles are congruent because all three sides are congruent. (SSS)
AB is congruent to CD
AD is congruent to BC
AC is congruent to AC

Because we know that the total weight of the feed is 60 pounds, we can call the weight of one of the feeds x and the other 60-x. Let's say x is the blue nag feed. Then...
Protein in blue nag = 0.17x
Protein in green pasture = 0.25 (60-x) = 15 - 0.25x
Total...

There are 52 cards, of which 13 are clubs. So the probability of drawing a club is 13/52 = 0.25 = 25%.

Use the formula V = P * e ^ rt, where V = final value, P = principal, e = 2.71828..., r = annual percentage rate compounded continuously, and t = time in years.
1.125 = 0.900 * e ^ rt
Divide both sides by 0.900.
1.25 = e ^ rt
So we know the final...

s = liters saccharine, w = liters of water.
s / (s + w) = 0.45
s + w = 89.
We then add x additional liters of water.
s / (s + w + x) = 0.40.
Cross-multiply.
s = 0.45 (s + w)
s = 0.40 (s + w + x)
Because both equations are equal to s they must be equal to each other.
0.45 (s + w) = 0.40 (s +...

If a number is 128 percent too high, that means it is 228 percent of the actual number.
So set up a ratio and cross multiply.
9120 / 228 = x / 100
912000 = 228x
x = 4000

Assuming the die is fair, past rolls do not matter. There are six sides, and four of them are greater than 2. The probability is 4/6 or 2/3.

Think about it. There is one way (1234) to choose four out of four, four ways (123, 124, 134, 234) to choose three out of four, six ways (12, 13, 14, 23, 24, 34) to choose two out of four, and four ways (1, 2, 3, 4) to choose one out of four. Fifteen possible combinations in all.
You...

We know that s + r = 17, and that 5s + 7r = 111.
Express either variable in terms of the other, for example, s = 17 - r. Then substitute into second equation.
So 5 (17 - r) + 7r = 111
85 - 5r + 7r = 111
2r = 26
r...

We can use the quadratic formula.
6x^2 + 11x = 2
6x^2 + 11x - 2 = 0
-11 +/- square root of (11^2 - 4*4*(-2)) / (2*6)
-11 +/- square root of (121 + 48) / 12
-11 +/- square root of 169 / 12
(-11...

We know the two runners are closing at a combined rate of 12mph and that the trail is 8 miles long. So the runners will meet after 8/12 hour = 2/3 hour = 40 minutes.
Check: In 2/3 of an hour, runner 1 will cover 3 1/3 miles and runner 2 will cover 4 2/3 miles. 3...

Scores are x and x + 9
x + 9 = 56% of total and x = 44%
Set up a proportion and cross-multiply:
x / 44 = (x + 9) / 56
56x = 44 (x + 9)
56x = 44x + 396
12x = 396
x = 33
So...

Shorter leg = x
Longer leg = 3x + 3
Hypotenuse = 3x + 4
x^2 + (3x + 3)^2 = (3x + 4)^2
x^2 + (9x^2 + 18x + 9) = (9x^2 + 24x + 16)
x^2 - 6x - 7 = 0
(x - 7)(x + 1) = 0
x = 7 or -1
Disregard...

Use the distance formula (Pythagorean theorem) to calculate the distances between each point and the center point. If the two distances are equal, the common distance is the radius of the circle.
square root of ((-8 - -2)^2 + (7 - -1)^2) = square root of (36 + 64) = 10
square...